MathDB
2019 Individual #11

Source:

May 1, 2022
2019 Individual

Problem Statement

An integer NN which satisfies exactly three of the four following conditions is called two-good.  ~
(I) NN is divisible by 22 (II) NN is divisible by 44 (III) NN is divisible by 88 (IV) NN is divisible by 1616  ~ How many integers between 11 and 100100, inclusive, are two-good?
<spanclass=latexbold>(A)</span>6<spanclass=latexbold>(B)</span>7<spanclass=latexbold>(C)</span>8<spanclass=latexbold>(D)</span>9<spanclass=latexbold>(E)</span>10<span class='latex-bold'>(A) </span>6\qquad<span class='latex-bold'>(B) </span>7\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>9\qquad<span class='latex-bold'>(E) </span>10